The formation of positronium in our Galaxy is well measured, and has led to important and unanswered questions on the origin of the positrons. In principle it should be possible to form analogous systems from $\mu$ and $\tau$ leptons, viz. true muonium and true tauonium. However the probability of formation for these systems is greatly reduced due to the intrinsically short lifetimes of the $\mu$ and $\tau$ leptons. Likewise, the decay of the atoms is hastened by the high probability of the constituent particles decaying. Nevertheless, if sufficient numbers of $\mu$ and $\tau$ pairs are produced in high energy astrophysical environments there may be significant production of true muonium and true tauonium, despite the small probabilities. This paper addresses this possibility. We have calculated the pair production spectra of $\mu$ and $\tau$ leptons from photon-photon annihilation and electron-positron annihilation in astrophysical environments. We have computed the cross sections for radiative recombination and direct annihilation of the pairs, and the decay constants for the various allowable decays, and the wavelengths and energies of the recombination and annihilation signatures. In this way we have calculated the probabilities for the formation of true muonium and true tauonium, and the branching ratios for the various observable signatures. We have estimated the expected fluxes from accretion disks around microquasars and active galactic nuclei, and from interactions of jets with clouds and stars. We find that accretion disks around stellar mass black holes in our own Galaxy should have observable signatures at x-ray and $\gamma$-ray energies that are in principle observable with current observatories.

• Received 27 January 2015

DOI:https://doi.org/10.1103/PhysRevD.91.123004